Improvement And Application Of Distance Measure And Coefficient Correlation Of Interval-Valued Hesitant Fuzzy Sets

The interval-valued hesitant fuzzy sets have a wide range of applications in many fields,so it is of great practical significance to study its distance measure and correlation coefficient.In the existing articles,only the interval endpoint value and the number of intervals are considered when calculating the distance,but the internal standard deviation of the interval-valued hesitant fuzzy sets are also important for the measurement of distance.This paper considers the internal standard deviation of the interval-valued hesitant fuzzy sets and the deviation distance between the interval-valued hesitant fuzzy sets,proposes a range formula for the interval-valued hesitant fuzzy sets with improved hesitance degree,and finally gives a numerical example to illustrate the rationality and superiority of the formula.When calculating the correlation coefficient,most of the existing literature only considers the membership degree in the hesitant fuzzy elements and the difference between the left and right endpoints of the interval between the hesitant fuzzy elements of the interval value,and requires that the number of values and intervals in the elements corresponding to each attribute are equal,resulting in a narrow application range of the correlation coefficient formula and certain limitations.According to the generalization of the calculation formula of the correlation coefficient in the hesitant fuzzy sets,the idea of interactive computation of two interval-valued hesitant fuzzy elements is proposed,which breaks the limitation of requiring the number of intervals to be consistent,and the internal standard deviation of the hesitant fuzzy set is selected as the hesitance degree,and the correlation coefficient calculation formula of the hesitant fuzzy set with hesitation is proposed,and special treatment is carried out for the situation when each element in the hesitant fuzzy set has only one value(resulting in the denominator of the hesitation part is 0).Finally,it is generalized to the calculation of the correlation coefficient of the interval-valued hesitant fuzzy sets,so that the calculation of the correlation coefficient is more reasonable and effective.